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Hermann Minkowski
Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, or Russian. He created and developed the geometry of numbers and elements of convex geometry, and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity. Minkowski is perhaps best known for his foundational work describing space and time as a four-dimensional space, now known as " Minkowski spacetime", which facilitated geometric interpretations of Albert Einstein's special theory of relativity (1905). Personal life and family Hermann Minkowski was born in the town of Aleksota, the Suwałki Governorate, the Kingdom of Poland, since 1864 part of the Russian Empire, to Lewin Boruch Minkowski, a merchant who subsidized the building of the choral synagogue in Kovno, and Rachel Taub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aleksotas
The Aleksotas Eldership () is an eldership in the southern section of the city of Kaunas, Lithuania, bordering the left bank of the Nemunas River. Its population in 2006 was 21,694. The elderate borders Vilijampolė and Centras in the north, Šančiai and Panemunė in the east, Garliava in the south as well as Akademija in the west. History There is evidence that during pre-Christian times a pagan shrine was located here. The suburb was founded in 1408, when Vytautas the Great granted the woods that stood here to the city of Kaunas. Until the 16th century it was called ''Svirbigala'', derived from the rivulet Svirbė. The name Aleksotas was used from the 16th century on, and is thought to be derived from the word ''aleksotai'' (shipyards) since many Nemunas River transport operations were located there. After the final Partition of the Polish-Lithuanian Commonwealth in 1795, Aleksotas, unlike most of Lithuania, became part of Prussia, until 1807 when Napoleon incorporate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry Of Numbers
Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice (group), lattice in \mathbb R^n, and the study of these lattices provides fundamental information on algebraic numbers. initiated this line of research at the age of 26 in his work ''The Geometry of Numbers''. The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational number, irrational quantity. Minkowski's results Suppose that \Gamma is a Lattice (group), lattice in n-dimensional Euclidean space \mathbb^n and K is a convex centrally symmetric body. Minkowski's theorem, sometimes called Minkowski's first theorem, states that if \operatorname (K)>2^n \operatorname(\mathbb^n/\Gamma), then K contains a nonzero vector in \Gamma. The successive minimum \lamb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russia
Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders of Russia, land borders with fourteen countries. Russia is the List of European countries by population, most populous country in Europe and the List of countries and dependencies by population, ninth-most populous country in the world. It is a Urbanization by sovereign state, highly urbanised country, with sixteen of its urban areas having more than 1 million inhabitants. Moscow, the List of metropolitan areas in Europe, most populous metropolitan area in Europe, is the capital and List of cities and towns in Russia by population, largest city of Russia, while Saint Petersburg is its second-largest city and Society and culture in Saint Petersburg, cultural centre. Human settlement on the territory of modern Russia dates back to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukraine to the east, Slovakia and the Czech Republic to the south, and Germany to the west. The territory has a varied landscape, diverse ecosystems, and a temperate climate. Poland is composed of Voivodeships of Poland, sixteen voivodeships and is the fifth most populous member state of the European Union (EU), with over 38 million people, and the List of European countries by area, fifth largest EU country by area, covering . The capital and List of cities and towns in Poland, largest city is Warsaw; other major cities include Kraków, Wrocław, Łódź, Poznań, and Gdańsk. Prehistory and protohistory of Poland, Prehistoric human activity on Polish soil dates to the Lower Paleolithic, with continuous settlement since the end of the Last Gla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germany
Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total population of over 84 million in an area of , making it the most populous member state of the European Union. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The Capital of Germany, nation's capital and List of cities in Germany by population, most populous city is Berlin and its main financial centre is Frankfurt; the largest urban area is the Ruhr. Settlement in the territory of modern Germany began in the Lower Paleolithic, with various tribes inhabiting it from the Neolithic onward, chiefly the Celts. Various Germanic peoples, Germanic tribes have inhabited the northern parts of modern Germany since classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Zürich
The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of theology, law, medicine which go back to 1525, and a new Faculty (division), faculty of philosophy. Currently, the university has seven faculties: Philosophy, Medicine, Human Medicine, Economic Sciences, Law, Mathematics and Natural Sciences, Theology and Veterinary Medicine. The university offers the widest range of subjects and courses of any Swiss higher education institution. History The University of Zurich was founded on April 29, 1833, when the existing colleges of theology, the Carolinum, Zurich, ''Carolinum'' founded by Huldrych Zwingli in 1525, law and medicine were merged with a new faculty of Philosophy. It was the first university in Europe to be founded by the state rather than a monarch or church. Its Latin name is reminiscen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Königsberg
The University of Königsberg () was the university of Königsberg in Duchy of Prussia, which was a fief of Poland. It was founded in 1544 as the world's second Protestant Reformation, Protestant academy (after the University of Marburg) by Duke Albert, Duke of Prussia, Albert of Prussia and charted by the King Sigismund II Augustus. It was commonly known as the Albertina and served as a Protestant counterpart to the Catholic Jagiellonian University in Kraków. Following World War II, the city of Königsberg was transferred to the Soviet Union according to the 1945 Potsdam Agreement, and renamed Kaliningrad in 1946. The Albertina was closed and the remaining German population Flight and expulsion of Germans (1944–1950), expelled, by the terms of the Potsdam Agreement. Today, the Immanuel Kant Baltic Federal University in Kaliningrad claims to maintain the traditions of the Albertina. History Albert, former Grand Master of the Teutonic Order and first Duchy of Prussia, Duke of P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random House Webster's Unabridged Dictionary
''Random House Webster's Unabridged Dictionary'' is a large American dictionary, first published in 1966 as ''The Random House Dictionary of the English Language: The Unabridged Edition''. Edited by Editor-in-chief Jess Stein, it contained 315,000 entries in 2256 pages, as well as 2400 illustrations. The CD-ROM version in 1994 also included 120,000 spoken pronunciations. History The Random House publishing company entered the reference book market after World War II. They acquired rights to the ''Century Dictionary'' and the ''Dictionary of American English'', both out of print. Their first dictionary was Clarence Barnhart's ''American College Dictionary'', published in 1947, and based primarily on ''The New Century Dictionary'', an abridgment of the ''Century''. In the late 1950s, it was decided to publish an expansion of the ''American College Dictionary'', which had been modestly updated with each reprinting since its publication. Under editors Jess Stein and Laurence Urdan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number ''p''/''q'' is a "good" approximation of a real number ''α'' if the absolute value of the difference between ''p''/''q'' and ''α'' may not decrease if ''p''/''q'' is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of simple continued fractions. Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Space
In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds". Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.This makes spacetime distance an inva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
